The Earth's dance partner

Ever heard of 3753 Cruithne?

I hadn't, which is surprising considering my obsession with astronomy.  It's an asteroid which is in a 1:1 orbital resonance with Earth -- in simpler terms, it is co-orbital.  It's sometimes been called "Earth's second moon," which is inaccurate because it doesn't orbit the Earth; in fact, its actual orbit is highly elliptical.  At its perigee, 3753 Cruithne is near the orbit of Mercury, and is outside the orbit of Mars at its apogee.

[Nota bene: the name "Cruithne" is from Gaelic, and because of the strange letter-to-phoneme correspondence in the Gaelic language, is pronounced "kroo-in-ya."  It's the name of an obscure king of the ancient Picts; its discoverer, astronomer Duncan Waldron, is Scottish, which probably explains the choice.]

Orbital resonance is one restricted solution to the more general three-body problem, which has yet to be solved by physicists.  The orbital interactions between two objects is thoroughly understood; add a third, and suddenly the math kind of blows up in your face.  You can run computer simulations starting with three objects of specific masses and velocities and see what happens, but a general set of equations governing any three (or more) body system has proven to be impossibly complex.  It's known that a few starting points generate stable orbits (resonance being one of those), and lots more of them prove unstable and eventually result in the objects colliding or flying apart, but trying to come up with the overarching mathematical scheme is currently out of reach.

3753 Cruithne's orbit, at least from our vantage point here on Earth, is a strange one.  If you were out in space, looking down on the Solar System, it wouldn't seem odd; an ellipse, tilted at a little less than twenty degrees away from the orbital plane of Earth:

[Image licensed under the Creative Commons Derivative work: User:Jecowa, Orbits of Cruithne and Earth, CC BY-SA 3.0]

But because of the weird perspective of being in a non-inertial (accelerated) reference frame, what we see on Earth is quite different.  As we watch 3753 Cruithne, it appears to be traveling in a bean-shaped orbit, first approaching us and then backing away as if we'd said something inappropriate:

[Image licensed under the Creative Commons User:Jecowa, Horseshoe orbit of Cruithne from the perspective of Earth, CC BY-SA 3.0]

Makes me realize how hard it is to come up with any reasonable model of moving objects in non-inertial reference frames.  Looking at 3753 Cruithne's strange wanderings almost leaves me sympathetic with Ptolemy and his nested epicycles.  (Isaac Newton, who understood the problem better than just about anyone else, wasn't nearly so forgiving, and called Ptolemy "an outrageous fraud.")

Its orbit classifies it as an Aten asteroid, a group of asteroids whose orbits cross that of the Earth.  For those of you who are of an apocalyptic bent, however, no need to lose sleep over 3753 Cruithne; its orbital tilt makes it no threat.  Its position has been run forward by computer models for thousands of years, and it has a zero chance of striking Earth.

That's assuming the orbital resonance remains stable, of course, and there's no guarantee it will.  There are other players in this gravitational game of pinball besides the Earth and the Sun; Venus and Mercury also come close to 3753 Cruithne on occasion, and a near pass could give the asteroid enough of a gravitational tug to destroy the resonance and destabilize the orbit.  The great likelihood if this happens, though, is it falling into the Sun or being flung out of the Solar System entirely; the chance of some gravitational slingshot effect propelling it into the Earth is about as close to zero as you can calculate.

So that's today's astronomical oddity that I, at least, had never heard of.  An asteroid in an ongoing celestial dance with the Earth.  Just goes to show that to find strange new stuff out in space, you don't need to peer out at the far reaches of the universe -- there's enough right here near home to keep the astronomers busy for a long while.

****************************************

Chewed up and spat out

Seems like I've featured a lot of research about astrophysics here at Skeptophilia lately, and that's not only because I'm really interested in it, but because the astrophysicists keep discovering stuff that is downright amazing.

Consider two papers last week highlighting different bizarre behaviors of one of the weirdest beasts in the cosmic zoo -- black holes. 

Since the first serious proposal of their existence, by German physicist Karl Schwarzschild in 1916, they've captivated the imagination.  Not only are they created in supernovas -- surely the most spectacular events in the universe -- their intense gravitational warping of space makes it impossible for anything, even light, to escape.  If you were falling into one (not recommended), time would slow down, at least as perceived by someone watching you from a safe distance.  From your perspective, though, your own watch would continue to run normally, until it (and you) succumbed to spaghettification -- yes, that's actually what the astrophysicists call it -- the point where the tidal forces across even such a short distance as the one between your head and your feet became sufficient to stretch you into the universe's most horrifying pasta.

As strange and terrifying as they are, they were thought for a long time to be physically quite simple; physicist John Archibald Wheeler said that "black holes have no hair," by which he meant that they have no arbitrary differences between each other that cannot be accounted for by three externally-observable parameters: their mass, angular momentum, and electric charge.  It took no less a luminary than Stephen Hawking to demonstrate that this wasn't true.  In 1974 he showed that (contrary to the picture of a black hole as a one-way-only object) they slowly evaporate through a phenomenon now called Hawking radiation in his honor.  The general idea here is that the extremely warped space near the event horizon generates sufficient energy to facilitate significant pair production -- creation of particle/antiparticle pairs.  Almost always, those pairs recombine and mutually annihilate in a fraction of a second after creation, so they're called "virtual particles" that have a measurable effect on ordinary matter but no long-term reality.  However, in the vicinity of a black hole, things are different.  Because of the extraordinary gravitational field at the event horizon, sometimes there's enough time for the two particles in the pair to separate sufficiently that one of them crosses the event horizon and the other doesn't.  At that point, the one that's fallen in is doomed; the other one just keeps moving away -- and that's the Hawking radiation.  

But what this does is robs a small bit of the mass/energy from the black hole, so its volume decreases.  What Hawking showed is that black holes actually evaporate.  It's on a huge time scale; a massive black hole has a life span many times longer than the current age of the universe.  But it suggests that everything -- even something as seemingly permanent as a black hole -- has a finite life span.

[Image is in the Public Domain courtesy of NASA/JPL]

Even that, though, doesn't begin to plumb the depths of the weirdness of these things.  Take for example the two papers I referenced earlier, each of which shows an only partially-explained behavior of black holes.

In the first, that appeared in The Astrophysical Journal, researchers looked at the odd behavior of an object called X-7 that is close to Sagittarius A*, the massive black hole at the center of the Milky Way galaxy.  X-7 is a cloud of gas and dust about fifty times the mass of the Earth, and is so close to Sagittarius A* that it orbits it once every 170 years.  The tidal forces are spaghettifying X-7 -- fast enough to observe in real time.

"No other object in this region has shown such an extreme evolution," said Anna Ciurlo of UCLA, who is the paper’s lead author.  "It started off comet-shaped and people thought maybe it got that shape from stellar winds or jets of particles from the black hole.  But as we followed it for twenty years we saw it becoming more elongated.  Something must have put this cloud on its particular path with its particular orientation."

From its current trajectory, the researchers think that it will get close enough to the black hole by 2036 that it will be torn apart completely.

If X-7 is being chewed up, there's another place in the universe where a black hole has been spat out.  The galaxy RCP 28, 7.5 billion light years from Earth, appears to be undergoing something cataclysmic; its central black hole, with an estimated mass of twenty million times that of the Sun, has been ejected from the middle and is moving away at a speed of 5.6 million kilometers per hour, pulling along a streamer of stars behind it like the tail of a comet.

What could possibly slingshot an object that massive at such high velocities remains to be seen; the researchers think it was in some kind of unstable orbit with two or more massive bodies.  (As I described in a post a couple of years ago, the three-body problem -- the mathematics of three or more objects of similar masses orbiting a common center of gravity -- is one of the most famous unsolved problems in classical mechanics, and models show that most of the time, these sorts of configurations are unstable.)  But the authors are clear that more study is needed to confirm the analysis, and then, to come up with an explanation for what exactly is going on.

In any case, what's obvious is that we've only scratched the surface of these strange objects.  Every time we look up into the star-spangled sky, we find new and amazing things to wonder at.  The astrophysicists, I think, are in for a long and exciting ride.

****************************************

The ghoul's head and the three-body problem

Ever heard of Algol?

Known to astronomers as Beta Persei, it's the second-brightest star in the constellation of Perseus.  It was singled out as strange a long time ago.  Even in a small telescope it looks like a single star, but in 1881 it became the first identified eclipsing binary, a pair of stars orbiting around a common center of gravity with the orbital plane lined up so that from our perspective, one passes in front of the other.  Because one of the stars is dimmer than the other, when the dimmer one crosses in front of the brighter one, the brightness of the pair appears to diminish -- the transit takes ten hours and happens every 2.86 days, so it's regular as clockwork.

The first certain mention of Algol's variability was by Italian astronomer Geminiano Montanari in 1667, but way before that the star had a reputation for being uncanny.  The name Algol comes from the Arabic رأس الغول (raʾs al-ghūl) -- "the head of the ghoul."  The Greeks, who named the constellation in which it resides Perseus, thought that Algol was the Gorgon's head that the hero was carrying.  The ancient Hebrews called it Rōsh ha Sāṭān (Satan's head).  These are similar enough that they probably come from a common source, but the Chinese as well thought there was something evil about it; they called Algol and the stars surrounding it Dà Líng -- the Mausoleum.

So even if there's no certain evidence that the ancients knew about Algol's odd variability, it seems pretty likely.

What no one realized until recently is that Algol is weirder even than that.  To see just how strange it is, first a brief physics lesson.

Some of the great names of physics and astronomy in the sixteenth and seventeenth centuries -- Galileo Galilei, Tycho Brahe, Johannes Kepler, and Isaac Newton, especially -- used highly accurate data on planetary positions to conclude that the planets in the Solar System go around the Sun in elliptical orbits, all powered by the Universal Law of Gravitation.  The mathematical model they came up with worked to a high degree of accuracy, allowing earthbound astronomers to predict where the planets were in the sky, and also such phenomena as eclipses.

Lucky for them, though, that the Sun is so massive.  Because the Sun is huge -- it has a thousand times more mass than the largest planet, Jupiter -- its gravitational pull is big enough that it swamps the pull the planets exert on each other.  For most purposes, you can treat each orbit as independent two-body problems; you can (for example) look at the masses, velocities, and distances between the Sun and Saturn and ignore everything else for the time being.  (Interestingly, it's the slight deviation of the orbit of Uranus from the predictions of its position using the two-body solution that led astronomers to deduce that there must be another massive planet out there pulling on it -- and in 1846 Neptune was observed for the first time, right where the deviations suggested it would be.)

I said it was "lucky" that the mass imbalance is so large, but I haven't told you how lucky.  It turns out that all you have to do is add one more object of close to the same size, and you now have the three-body problem -- a big problem, because physicists have been unable to find a general solution to the equations it generates.  You can pick the parameters (mass, separation distance, initial velocity, and so on) and have a computer model what the orbits would look like, but there's no overarching set of mathematical equations that physicists can use on any other system with different parameters.  The unifying model just doesn't exist, or at least hasn't been discovered yet.

Worse still, most individual three-body systems generate chaotic orbits.  Here's a rather mesmerizing gif showing one of them:

[Image is licensed under the Creative Commons Dnttllthmmnm, Three-body Problem Animation with COM, CC BY-SA 4.0]

The reason this comes up  is a paper in The Astrophysical Journal showing that Algol isn't a simple double star system, with two stars orbiting their common center of gravity like Newton said.  In the 1950s astronomers figured out that the known binary system (Algol A and Algol B) is in an orbit with a third star (Algol C), with the whole trio orbiting their center of gravity once every 1.86 years, and presumably tracing out some kind of bizarre Spirograph pattern like the one in the gif.

But the recent paper showed that it's not even that simple.  Algol isn't a weird, chaotic three-star system.

The "star" we call Algol is apparently made up of at least seven stars all moving in a complex dance around their collective center of gravity.

Algol is in our stellar neighborhood -- only ninety light years away -- so why haven't they been observed until now?

"The paradox is that Algol A is 'too bright,' " said astrophysicist Lauri Jetsu, author of the paper, in an interview with Science Daily.  "It can hide these new companion candidate stars even from our most powerful modern space telescopes, just like our Sun can hide all other stars during daytime...  Even the cutting-edge equipment onboard the Gaia satellite could not detect these new companion candidates.  Future interferometric observations may be used to directly confirm the existence of at least some of Algol's companions."

I find it fascinating that even in a part of physics that is usually considered pretty well sussed-out -- classical mechanics, the study of objects in motion -- there are unsolved problems that the experts consider very close to intractable.  Further reinforcing the notion that the universe doesn't seem to feel obliged to choose how it acts based upon whether humans find it comprehensible.  It does what it does, leaving us to try to explain how on earth (or off it) that kind of thing could happen -- in this case, seven massive objects all whirling around each other in apparently stable orbits.

It's a little like the famous (if apocryphal) story about bumblebees -- that physicists have analyzed their mass, wing size, wing beat frequency, and so on, and have come to the conclusion that bumblebees can't fly.  The bumblebees, not knowing this, go ahead and fly anyway.  Here, the seven members of the Algol system are apparently unaware that the steps of their cosmic dance is beyond what our current physics can explain, but it doesn't stop them from dancing.

Think of that the next time you look at the night sky, and see the bright blue pinpoint of the ghoul's head twinkling against the blackness.

**********************************

My master's degree is in historical linguistics, with a focus on Scandinavia and Great Britain (and the interactions between them) -- so it was with great interest that I read Cat Jarman's book River Kings: A New History of Vikings from Scandinavia to the Silk Road.

Jarman, who is an archaeologist working for the University of Bristol and the Scandinavian Museum of Cultural History of the University of Oslo, is one of the world's experts on the Viking Age.  She does a great job of de-mythologizing these wide-traveling raiders, explorers, and merchants, taking them out of the caricature depictions of guys with blond braids and horned helmets into the reality of a complex, dynamic culture that impacted lands and people from Labrador to China.

River Kings is a brilliantly-written analysis of an often-misunderstood group -- beginning with the fact that "Viking" isn't an ethnic designation, but an occupation -- and tracing artifacts they left behind traveling between their homeland in Sweden, Norway, and Denmark to Iceland, the Hebrides, Normandy, the Silk Road, and Russia.  (In fact, the Rus -- the people who founded, and gave their name to, Russia -- were Scandinavian explorers who settled in what is now the Ukraine and western Russia, intermarrying with the Slavic population there and eventually forming a unique melded culture.)

If you are interested in the Vikings or in European history in general, you should put Jarman's book in your to-read list.  It goes a long way toward replacing the legendary status of these fierce, sea-going people with a historically-accurate reality that is just as fascinating.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

A planetary Tilt-o-Whirl

A long-standing unsolved puzzle in physics is the three-body problem, which despite its name is not about a ménage-à-trois.  It has to do with calculating the trajectory of orbits of three objects around a common center of mass, and despite many years of study, the equations it generates seem to have no general solution.

There are specific solutions for objects of a particular mass starting out with a particular set of coordinates and velocities, and lots of them result in highly unstable orbits.  Take, for example, this one, which involves three objects of equal masses, starting out with zero velocity and sitting at the vertices of a scalene triangle:

[Animation licensed under the Creative Commons Dnttllthmmnm, Three-body Problem Animation with COM, CC BY-SA 4.0]

It's a problem that has application to our understanding of double and triple star systems, which seem to be quite common out there in the cosmos.  For people like me, who are fascinated with the possibility of extraterrestrial life, it's especially important -- because if the majority of planets in orbit around a double star (or worse, a triple star) follow unstable trajectories, that would represent a considerable impediment to the evolution of life.  Such planets would have wildly fluctuating climates, a possibility that resulted in a plot twist on the generally abysmal 1960s science fiction show Lost in Space, even though when it came up (1) the writers evidently didn't know the difference between a planet's rotation and its revolution, with the result that the blazing heat wave and freezing cold only lasted a few hours each, and (2) in subsequent episodes they conveniently forgot all about it, and it was never mentioned again.

Be that as it may, now that we have a vastly-improved ability to detect extrasolar planets and determine their orbits around their host star(s), it's given us more information about what kinds of trajectories these complex systems can take.  For example, consider the system GW Orionis, which was the subject of a paper last week in Science.

GW Orionis is a trio of young stars, two of which are quite close together, and the third further away.  The two closer ones are whirling around pretty quickly, and the third making long swoopy dives in toward (and then away from) the others.

Complicated enough, but add to that a set of proto-planetary rings.  Three of them, in fact.  And unlike our own rather sedate star system, where all the planets except for Pluto are orbiting within under seven degrees' tilt with respect to a flat plane -- even Pluto's orbit is only tilted by fifteen degrees -- this system is kind of all over the place.

Here's an artist's conception of what GW Orionis looks like, based on the measurements and observations we have:

[Image courtesy of L. Calçada/ESO, S. Kraus et al., University of Exeter]

Pretty cool-looking.  Given our lack of knowledge of (in this case) six-body problems -- the three stars and the three planetary rings -- no one knows for sure if this is going to be a long-lasting, stable system, or if it will eventually collapse or fly apart.  It seems likely that the system would be a planetary Tilt-o-Whirl, and any orbits formed would be as chaotic as the animation I included above, but honestly, that's just a guess.

However, it's entertaining to think of what life would be like on a planet with three suns in the sky.  One more even than Tatooine:

The more we scan the skies, the more awe-inspiring things we find.  I'm glad to live in a time when our ability to study the stars has improved to the point that we're able to consider not just systems like our own, but the vast array of possibilities that are out there.  One thing's for certain: if you are into astronomy, you'll never be bored.

**************************************

Humans have always looked up to the skies.  Art from millennia ago record the positions of the stars and planets -- and one-off astronomical events like comets, eclipses, and supernovas.

And our livelihoods were once tied to those observations.  Calendars based on star positions gave the ancient Egyptians the knowledge of when to expect the Nile River to flood, allowing them to prepare to utilize every drop of that precious water in a climate where rain was rare indeed.  When to plant, when to harvest, when to start storing food -- all were directed from above.

As Carl Sagan so evocatively put it, "It is no wonder that our ancestors worshiped the stars.  For we are their children."

In her new book The Human Cosmos: Civilization and the Stars, scientist and author Jo Marchant looks at this connection through history, from the time of the Lascaux Cave Paintings to the building of Stonehenge to the medieval attempts to impose a "perfect" mathematics on the movement of heavenly objects to today's cutting edge astronomy and astrophysics.  In a journey through history and prehistory, she tells the very human story of our attempts to comprehend what is happening in the skies over our heads -- and how our mechanized lives today have disconnected us from this deep and fundamental understanding.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Homing in on Tatooine

I remember the first time I ran into the concept that the Earth's relatively circular orbit might not be universal amongst the planets out there in the universe.

I shudder to admit that it was on the generally abysmal 1960s science fiction series Lost in Space.  The brave crew of the Jupiter 2 are stranded on a strange planet, and initially the whole place seems to be a frozen wasteland.  But after a journey via their "chariot" (as they call their tank-like wheeled transport vehicle), they find the temperature is seesawing wildly -- at first it seems to be heading to cold temperatures that will eliminate all possibility of life, but unexpectedly the mercury begins to rise, and what was a crossing on solid ice turns into a treacherous sea voyage (the chariot, fortunately, has amphibious capabilities).

The explanation we're given is that the planet they're on has a very elliptical orbit, so it experiences huge temperature changes.  Unfortunately, the writers of the show apparently did not understand that there's a difference between a planet's rotation and its revolution, so they depict the excruciatingly hot temperatures when the planet is at its perigee as only lasting a minute or two, so all the Robinsons had to do was hide under a reflective shelter for a little bit to avoid getting cooked.

So good idea, lousy execution, which can be said of much of that series.

A more fundamentally startling change in my perception of what it'd look like on another planet occurred when I saw Star Wars for the first time, and hit the iconic scene where Luke is looking toward the horizon as sunset occurs on Tatooine -- and there are two suns in the sky.  Tatooine, it seems, orbits a binary star -- something I'd honestly never thought about before then.

Being a science nerd type, I wondered what the shape of a planet's orbit would be if it were moving around two centers of gravity, and found pretty quickly that my rudimentary knowledge of Newton's Laws and Kepler's Law were insufficient to figure it out.

Turns out I wasn't alone; physicists have been wrestling with the three-body problem for a couple of hundred years, and there is no general solution for it.  Three objects orbiting a common center of gravity results in a chaotic system, where the paths of each depend strongly on initial conditions (and some configurations are unstable and result in either collisions or one of the objects being ejected from the system).

It is known, however, that there are points in a three-body system called Lagrange points (after their discoverer, the French mathematician and astronomer Joseph-Louis Lagrange) which result in a stable configuration in which each of the orbiting bodies stays in the same locked position relative to the other, so the entire system seems to turn as one.  Some of the moons of Jupiter (the so-called Trojan moons) sit at the Lagrange points for that system, a pattern that seems to be stable indefinitely.  (Note that from the Earth perspective, an object at the L3 Lagrange point would never be visible -- leading conspiracy wackos to postulate that it could be a place for alien spacecraft to be hiding.)

[Image licensed under the Creative Commons Xander89, Lagrange points simple, CC BY 3.0]

Things only get worse when you add additional objects.  The only way to approximate the configuration of the orbits is to input the specific initial parameters and use computer modeling software to determine a solution; there is no general set of equations to predict what it will look like.

What brings this up is a paper this week in The Astrophysical Journal that went beyond the theoretical, and found actual data from binary star systems with planets to see what the various orbits looked like.  In "The Degree of Alignment between Circumbinary Disks and Their Binary Hosts," by a team led by Ian Czekala of the University of California - Berkeley, we read about new observations from the Atacama Large Millimeter/submillimeter Array (ALMA), which tells us that not only might objects orbiting a binary star exhibit chaotic paths, they might not all orbit in the same plane.

Because of the way planets form -- coalescence of dust and debris from a flat ring surrounding the host star -- planetary systems seem mostly to be aligned with each other.  In our own Solar System, the eight planets all orbit within seven degrees of the Earth's orbital plane (excluding, sadly, Pluto, which still hasn't recovered its planet status, and has an orbital tilt of just over seventeen degrees).

But apparently there are exceptions.  Some binary stars have planets that orbit in a highly tilted ellipse with respect to the orbit of the two stars around their own center of mass.  How this could happen -- whether the planets condensed from a ring that was already tilted for some reason, or that the three-body chaos warped the orbits after formation -- isn't known.  "We want to use existing and coming facilities like ALMA and the next generation Very Large Array to study disk structures at exquisite levels of precision," study lead author Czekala said, "and try to understand how warped or tilted disks affect the planet formation environment and how this might influence the population of planets that form within these disks."

Which is pretty cool.  While it won't solve the more general difficulty of the three-body problem (and the four-, five-, six-, etc. body problems), it will at least give some empirical data to go on with which to analyze other systems ALMA finds.

So we're homing in on Tatooine.  For what it's worth, it looks like the overall situation might be more similar to Star Wars than it is to Lost in Space.

Which is a good thing in a variety of respects.

*****************************

Any guesses as to what was the deadliest natural disaster in United States history?

I'd speculate that if a poll was taken on the street, the odds-on favorites would be Hurricane Katrina, Hurricane Camille, and the Great San Francisco Earthquake.  None of these are correct, though -- the answer is the 1900 Galveston hurricane, that killed an estimated nine thousand people and basically wiped the city of Galveston off the map.  (Galveston was on its way to becoming the busiest and fastest-growing city in Texas; the hurricane was instrumental in switching this hub to Houston, a move that was never undone.)

In the wonderful book Isaac's Storm, we read about Galveston Weather Bureau director Isaac Cline, who tried unsuccessfully to warn people about the approaching hurricane -- a failure which led to a massive overhaul of how weather information was distributed around the United States, and also spurred an effort toward more accurate forecasting.  But author Erik Larson doesn't make this simply about meteorology; it's a story about people, and brings into sharp focus how personalities can play a huge role in determining the outcome of natural events.

It's a gripping read, about a catastrophe that remarkably few people know about.  If you have any interest in weather, climate, or history, read Isaac's Storm -- you won't be able to put it down.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]